Star trackers may be used as attitude determination instruments onboard satellites. In essence, a star tracker is a camera connected to a microcomputer located in a satellite. Using the camera to capture a sensed image of the sky, stars may be located and identified. The orientation of the satellite may be determined based on these observations. A star tracker automatically recognizes the star patterns in the field of view (FOV) of the camera and calculates the attitude with respect to the celestial sphere being orbited by the satellite.
The performance of a star tracker depends on many parameters. For example, performance may depend on the sensitivity to starlight, the FOV, the accuracy of the star centroiding algorithm, the star detection threshold, the number of stars in the FOV, the internal star catalog and the calibration process.
Star sensors fall into two categories: scanners and trackers. Scanners have a linear array of detectors that is scanned across the sky in a direction perpendicular to the span of the array. Trackers view the sky with a 2-dimensional detector array. Both of these systems collect a 2-dimensional image of the star field, the scanner by scanning and the tracker by staring.
Most star sensing systems are dedicated to scanning or tracking the sky. They have suitable signal-to-noise (S/N) ratios and spatial resolutions, so that stars may be detected and the images may be properly centroided to provide stellar locations in focal-plane coordinates.
Dedicated star scanners/trackers typically may use a star sensing algorithm that includes the following steps:                (1) Threshold the imagery at 5 times the RMS noise level to detect the stars in the image.        (2) Center a window on each resulting detection (3×3 pixels up to 11×1 pixels, typically).        (3) Estimate the background level by calculating the average value of samples from the 1-pixel wide frame that surrounds the window and, then subtract this level from all samples in the window.        (4) Calculate the centroid of the resulting data within the window to determine the star location.        
In an article, titled “Accuracy Performance of Star Trackers—A Tutorial” by Carl Christian Liebe, published by IEEE Transactions on Aerospace and Electronic Systems, Vol. 38, No. 2, April 2002, star detection is described. Liebe notes that principal contributors to the background signal noise are typically: read noise, and inhomogeneity of dark currents in the pixels. It may be possible to estimate the background noise as a standard deviation of all pixel values in a dark frame. A focal plane, which may include up to 106 pixels, may set the detection threshold of a star signal to an average background pixel value plus 5 times the standard deviation to avoid false positives. A star may then be detected if the brightest pixel in the star is above the set threshold.
The brightest pixel of a star depends on a point spread function (PSF) and position of the star. As an example, if the star image has a Gaussian PSF radius of 0.5 pixels and is centered on a pixel, then approximately 29% of the signal may be contained in the brightest pixel. If the radius of the Gaussian PSF is 1 pixel and the star is centered on a boundary between 4 pixels, however, then the brightest pixel may only contain 13% of the signal, approximately.
With respect to centroiding, Liebe notes that star trackers utilize subpixel centroiding to increase accuracy. In a focused image, a star appears as a point source, so all photoelectrons from the star are generated in a single pixel. If the optics are slightly defocused, however, the star may occupy several pixels. Defocusing, thus, facilitates calculating the center of the star with subpixel accuracy.
Initially, the image may be sifted for pixels that are above a predetermined threshold. Once a pixel is detected, a region of interest (ROI) window may be centered around the detected pixel. The average pixel value on the border may be calculated and subtracted from all other pixels in the ROI.
Instruments that are dedicated to perform star tracking and require very accurate pointing knowledge do not tolerate alignment uncertainty between the instrument's focal plane array (FPA) and the star. Additional algorithms may be necessary to increase accuracy between the instrument's FPA and a line pointing to the star.
When star sensing is performed with an instrument designed for imaging the earth, however, standard algorithms may not be good enough. Because the instrument's design is driven by requirements for obtaining good earth imagery, the ability to perform star sensing may be compromised.
Further complications may arise from the fact that stars are relatively dim compared to the high albedo portions of the sunlit earth. Thus, an earth imager is typically less sensitive to dim stars than a dedicated star sensor would be. Typical integration times for an earth imager may be 1000 times shorter than those of a dedicated star tracker. Also, a limited FOV in the earth imager may place additional constraints on the available stars, and the earth imager may have to rely on dimmer stars. Thus, the signal-to-noise ratio (SNR) of star signals from the earth imager may be lower than the SNR of a dedicated star sensor.
Current algorithms may not be able to reliably detect dim stars. The simple thresholding techniques used by current algorithms do not distinguish between light from stars and spikes due to noise or cosmic rays. These algorithms, therefore, may have high false alarm rates.
The maximum detector signal from a star is variable, since the energy may be split among several detectors. The fraction of the star energy collected by a detector depends on the star's path across the detector array, which is both variable and unknown. Current algorithms may use a fixed detection threshold that is perhaps five times the RMS value of the noise. These algorithms may not be able to detect dim stars having an SNR of five or less, and may be unreliable when detecting stars with an SNR of 10 or less, due to detector signal variations from the scan geometry.
Current algorithms may calculate the centroid of the detector samples within a window of a predetermined size that is expected to include only the star of interest. There may be no certainty, however, that all the star energy falls within this window. In addition, the inclusion of detector samples that contain little or no signal, skews the results and diminishes the accuracy.
Furthermore, the accuracy of current centroiding techniques may be diminished by noise spikes and may be completely destroyed when including pixels from nearby stars.
Scattered light in the optics or in the atmosphere may introduce background gradients in the detected data, depending on the relative positions of the star, earth, moon and sun. The background gradients may bias the star centroid, degrading accuracy for line-of-sight (LOS) angles that are relatively far from the sun (even 20-30 degrees away). This limits the stars that may properly be centroided with current algorithms.
The present invention addresses the above deficiencies and provides a solution to each one, as described below.